Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, Thomas A. Zang

Spectral Methods (eBook, PDF)

Evolution to Complex Geometries and Applications to Fluid Dynamics

• Format: PDF

Produktbeschreibung

Following up the seminal Spectral Methods in Fluid Dynamics, this book surveys the essential algorithmic and theoretical aspects of spectral methods for complex geometries. The chapter on spectral algorithms for incompressible flow is focused on those algorithms that have proven most useful in practice over the past two decades, has much greater coverage of algorithms for two or more non-periodic directions, and describes how to treat outflow boundaries. The material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 596
• Erscheinungstermin: 30. Juni 2007
• Englisch
• ISBN-13: 9783540307280
• Artikelnr.: 37370494

Autorenporträt

The authors are among the leading researchers in the field of computational fluid dynamics and have pioneered and promoted the "Spectral Methods in Fluid Dynamics".

Inhaltsangabe

Introduction.- Polynomial Approximation.- Basic Approaches to Constructing Spectral Methods.- Algebraic Systems and Solution Techniques.- Basic Approaches to Constructing Spectral Methods.- Algebraic Systems and Solution Techniques.- Global Approximation Results.- Theory of Stability and Convergence for Spectral Methods.- Analysis of Model Boundary-Value Problems.- Appendices A-E.

Rezensionen

Aus den Rezensionen: "... Schön ist ... dass die Autoren klar Tendenzen der spektralen Methoden der letzten 20 Jahre aufzeigen ... Im Einzelnen findet der interessierte Leser ... viele interessante Details zu Fragen der polynomialen Approximation und ... eine ausführliche Diskussion spektraler Methoden für zahlreiche Modellprobleme ... Insgesamt ist es ... sichtlich eine lohnenswerte Quelle für alle, die spektrale Methoden lieben. Und man kann gespannt sein, wie im Band 2 komplexere Gebiete und Probleme der Strömungsmechanik behandelt werden." (H.-G. Roos, in: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 2007, Vol. 87, Issue 1, S. 69)

From the reviews:

"In 2006 Canuto, Quarteroni and Zang presented us on 550 pages a new book on spectral methods ... . Now the second new book ('Evolution of complex geometrics and application to fluid dynamics', CHQZ3) is published and it contains further 600 pages on spectral methods. ... the book presents the actual state-of-the-art of spectral methods and yields for the active researcher a nice comprehensive survey on the modern theory and an excellent bibliography." (H.-G. Roos, Zentralblatt für Angewandte Mathematik und Mechanik, Vol. 88 (1), 2008)

"This book is ... dedicated to the application of spectral methods in fluid dynamics. ... the main objective of the new book is to modernize the classical spectral methods, accounting for advances in the theory and extensive application of multidomain spectral methods in fluid dynamics. ... This is a very useful book for graduate students, research mathematicians, geoscientists, physicists, and engineers interested in modern methods of numerical analysis, mathematical modeling and computational fluid dynamics." (Yuri N. Skiba, Mathematical Reviews, Issue 2009 d)